Chebyshev Formula

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Chebyshev Formula

 

a formula for the approximate computation of a definite integral:

The formula is accurate for polynomials of degree not greater than n – 1, where n is the number of nodes. The values of the x_i have been computed for some n. In the case of n = 9, for example, x₁ = –x₉ = 0.911589, x₂ = –x₈ = 0.601019, x₃ = –x₇ = 0.528762, x₄ = –x₆ = 0.167906, and x₅ = 0. For n = 8 and n > 9, the x_i have complex values; the Chebyshev formula can therefore be used only for n = 1, 2, 3, 4, 5, 6, 7, and 9. The for mula was derived by P. L. Chebyshev in 1873.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.